My wife was a flutist through elementary school and middle school and was the first freshman to play in wind ensemble in high school. She had braces from middle school through early high school and it didn't affect her embouchure at all. She went on to play as an adult.
She did get a little bit of soreness inside her lips. Putting wax over the braces avoided roughing up the inside of her mouth. (She had the old-school kind, not the newer Invisalign style.)
Her flute instructor and mentor was more concerned about her picking up piccolo parts. My wife liked them when nobody else wanted them, but her teacher advised against it because that seemed like it would have more of an affect on her embouchure than the braces.
The fact that you're aware of the issue will probably make you better at it. She says that nobody noticed when she got her braces off.